I’m looking into building a site for a contractor. Most of the site is static, but my question is about the dynamic part. I would like a client (of the contractor) to be able to log in as a user and be able to see a personal section of the website (viewable to him alone) with different data, graphs, and images that are specific to him and his project.

The data will obviously need to be set by an admin.

I am of course assuming that I will need to write a bit of code, but since I don’t have much experience with either Wordpress or Drupal, I wanted to get opinions as to which system would be better for my needs.

Drupal is considered to be both framework and CMS so coding will be easier.
Drupal has vast variety of modules which will help you a lot. I suggest looking into charts module for displaying charts into views and panels modules for managing layouts Content access or Organic groups modules for managing users. In included in core there is role and permissions system. There also modules which will allow you to set specific permissions for each content node.
If I where you I would use dashboard or panels modules to give users cognizable iGoogle like dashboard.